Geodesic
Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 925-963
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We provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation ∂φ ∂z+∂ ∂t[φ 2 /2]=w, where w is a bounded measurable function.

DOI : 10.1016/j.anihpc.2014.05.001
Keywords: Intrinsic Lipschitz graphs, Heisenberg groups, Lagrangian formulation, Scalar balance laws, Continuous solutions, Peano phenomenon 
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     author = {Bigolin, F. and Caravenna, L. and Serra Cassano, F.},
     title = {Intrinsic {Lipschitz} graphs in {Heisenberg} groups and continuous solutions of a balance equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Bigolin, F.; Caravenna, L.; Serra Cassano, F. Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 925-963. doi: 10.1016/j.anihpc.2014.05.001

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